Question

If the probability of A to fail in an examination is \[\frac{1}{5}\]  and that of B is \[\frac{3}{10}\] . Then, the probability that either A or B fails is

 

 

Options

• 1/2

• 11/25

•  19/50

•  none of these

   

Answer 1

19/50

Given:
P(A) = \[\frac{1}{5}\]

∴ P(A') = \[1 - \frac{1}{5} = \frac{4}{5}\]

P(B) = \[\frac{3}{10}\]

∴ P(B') = \[1 - \frac{3}{10} = \frac{7}{30}\]

Hence, required probability = P(A∩ B') + P(A'∩ B)

\[= \frac{1}{5} \times \frac{7}{10} + \frac{4}{5} \times \frac{3}{10}\]
\[ = \frac{7}{50} + \frac{12}{50}\]
\[ = \frac{19}{50}\]